Inadequacy of saphenous vein grafts for cross-femoral venous bypass Stephen G. Lalka, M D , Julia M. Lash, P h i ) , Joseph L. U n t h a n k , P h i ) , Valerie K. Lalka, R T , Dolores F. Cikrit, M D , Alan P. Sawchuk, M D , and Michael C. Dalsing, M D , Indianapolis, Ind. A mathematic m o d e l o f unilateral iliac vein obstruction was used to establish the theoretic
basis for selecting saphenous vein or a larger diameter prosthetic cross-femoral venous bypass graft for relief of obstructive venous hypertension. Common femoral vein resting and postexercise peak flows, and common femoral vein and saphenous vein diameters were measured in 18 healthy individuals and used to estimate the pressure gradient (dP) across 20 cm long cross-femoral venous bypass grafts of sapbenous vein or 4, 6, 8, 10, and 12 mm prosthetic conduits, in the presence of a transpelvic venous collateral network of varied cross section. The upper limits of normal for the gradients in our model (dPs,a) were set at 4 mm Hg for resting flows and 6 mm Hg after exercise. Mean sapbenous vein diameter was 4.3 +- 0.22 ram, which was 36.5% +- 1.73% of common femoral vein diameter. When the saphenous veins of two thirds of the individuals in our study were used as theoretic cross-femoral venous bypass conduits, > 80% of postobstruction peak cross-femoral venous bypass graft flow had to be carried by collaterals to maintain a gradient < dPst a. We demonstrated that 4.5 to 6.0 mm diameter saphenous cross-femoral venous bypass grafts would be bemodynamically efficacious in refieving venous hypertension, but only when implanted in parallel with an existing venous collateral network that limited the preoperative dI' to 4.5 to 7.5 mm Hg at resting flows and 7.0 to 11.5 nun Hg after exercise; only 44% ofsapbenous veins were adequate for cross-femoral venous bypass grafts by these criteria. Prosthetic cross-femoral venous bypass conduits of > 8 mm diameter eliminated venous hypertension even in the absence of collateral venous flow. ( J VAse Suv.~ 1991;13:622-30.)
Cross-femoral venous bypass (CFB) grafting for unilateral iliofemoral venous occlusion was introduced by Palma and Esperon ~ 30 years ago. Since then the literature records almost 400 o f these procedures performed for a variety o f indications: chronic venous hypertension resulting from remote iliofemoral deep venous thrombosis (most cases), incomplete restoration o f venous outflow after venous thrombectomy for acute iliofemoral thrombosis, trauma, iatrogenic operative injury, pelvic tumor ingrowth or extrinsic compression, radiation sequelae, retroperitoneal fibrosis, and "iliac vein compression syndrome" from the right c o m m o n iliac
From the Departments of Surgery, and Physiologyand Biophysics, Indiana University School of Medicine, Indianapolis. Presented at the Fourteenth Annual Meeting of the Midwestern Vascular Surgical Society, Toledo, Ohio, Sept. 14-15, 1990. Reprint requests: Stephen G. Lalka, MD, Assistant Professor of Surgery,Indiana UniversityMedicalCenter,Wishard Memorial Hospital OPE 310A, 1001 West 10th St., Indianapolis IN 46202 24/6/27614 622
artery overlying the left c o m m o n iliac vein at the pelvic brim. 2-4 As originally described and most commonly reported, the CFB is constructed by use of the contralateral saphenous vein transposed in subcutaneous suprapubic fashion to the obstructed limb. 1"2 Although unanimous agreement exists that autogenous venous conduits in peripheral venous reconstruction have better long-term patency than synthetic grafts, some investigators have noted that saphenous vein CFB grafts often provide inadequate symptomatic relief o f venous hypertension because o f the high resistance o f the small saphenous vein conduit. 4-7 Review o f the literature suggests that the ultimate test o f significance o f an iliac vein obstruction must be the physiologic demonstration o f an increased resistance to venous outflow; the best test is the comparison o f resting and postexercise femoral vein pressures between the obstructed and contralateral normal limbs. 811 In the opinion o f Browse et al.9 and May and DeWeese, ~° no iliac vein bypass procedure
Volume 13 Number 5 May 1991
should be performed without preoperative and postoperative femoral venous pressure measurements. Unfortunately, the few surgeons who have reported series of CFB procedures have not adequately documented the relationship between saphenous CFB graft patency, reduction in venous hypertension, and symptomatic relief. 2-4"6"7"~°-~ Because of the lack of clinical hemodynamic data verifying the efficacy of saphenous vein as a CFB conduit, we developed a mathematic model of unilateral iliac vein obstruction to establish a theoretic basis for selecting saphenous vein or a larger diameter prosthetic conduit for CFB. The validity of this mathematic model has previously been confirmed by in vivo canine studies. ~s PATIENTS A N D M E T H O D S Patient data
In 18 volunteer subjects (age 24 to 40 years; 11 men/7 women), an ultrasonic duplex scanner (ATL Ultramark 4, Advanced Technology Laboratories, Bothell, Wash.) was used to measure saphenous vein cross-sectional diameter, common femoral vein (CFV) diameter, and CFV peak velocity in one limb. These saphenous veins were free of varicosities, and there was no history of previous deep venous thrombosis in these limbs. The diameters and flows were measured in supine position, both at rest and immediately after standard treadmill exercise (2.5 mph and 10% grade for 5 minutes). This level of exercise was chosen to simulate venous outflow during normal daily physical activity. Saphenous vein diameter was measured at both the high- and low-thigh levels (n = 18) at rest, but was only recorded at the low-thigh level (n = 15) after exercise to record saphenous vein and CFV diameter and CFV velocity as simultaneously as possible after exercise. Theoretic hemodynamic analyses The equations used to construct our theoretic model of cross-femoral venous bypass are described in detail in the Appendix. Refer to Fig. 1 for a schematic representation of the mathematic model. The theoretic resistances of CFB grafts constructed with each subject's saphenous vein (using the average of their resting high- and low-thigh diameters) or prosthetic conduits of 4, 6, 8, 10, and 12 nun diameter, were calculated. Preexercise and postexercise CFV volume flows were calculated for each subject by use of the measured radius of the CFV and the measured peak venous flow velocity. The Poiseuille equation was then used to determine the
Saphenous vein for venous bypass 623
theoretic pressure gradients across 20 cm segments of saphenous vein and 4 to 12 mm prosthetic conduits by use of each individual's saphenous vein diameter and CFV flow. To account for the potential pressure dissipation associated with graft/femoral vein diameter mismatch at the inflow anastomosis when using hypodiametric CFB conduits, the Bernoulli principle was used to calculate the maximal additional theoretic pressure gradient at preexercise and postexercise peak CFV flows. For our series of mathematic simulations, several assumptions were necessary: (1) arterial inflow would not be chronically altered by iliac vein obstruction, based on animal data for femoral vein occlusion14; (2) total arterial inflow in both legs is equal, therefore the total venous outflow from the obstructed limb in a patient with unilateral iliac vein occlusion should be the same as in the contralateral normal limb, after a period of outflow redistribution by recruitment of superficial and deep ipsilateral and cross-over venous collaterals (hereafter termed transpelvic collaterals)~5; (3) under normal conditions CFV flow in both legs is equal and represents the same fraction of total venous outflow, therefore we can use the CFV flow measured in normal limbs as a clinically-relevant estimate of the redistributed venous flow that would either cross a CFB or be accommodated by newly recruited venous collaterals in a limb with iliac vein obstruction; and (4) because reports of clinical femoral venous pressure data indicate that the upper limits of the normal pressure gradient between limbs is 4 mm H g at rest and 6 mm Hg after exercise, s-12 these clinical standards (dPsta) were used in our model. The maximum flow that could be accommodated by each subject's saphenous vein at pressure gradients equal t o dPsta at rest and after exercise was calculated by means of the theoretic resistance of the graft. The fraction of an individual's preobstruction CFV flow that would have to be carried by collaterals, despite the presence of a saphenous CFB graft, to achieve a normal postoperative venous pressure differential between obstructed and contralateral normal limbs was then calculated for resting and postexercise peak flOWS.
To demonstrate the effects of venous collateralization alone on the femoral venous pressure gradient between limbs (hereafter termed the transfemoral pressure differential) in a patient with unilateral iliac vein occlusion, the theoretic venous pressure gradient was calculated for a wide range of collateral crosssectional area. We then calculated the total venous pressure differential between normal and abnormal
Journ~of VASCULAR SURGERY
624 Lalka et al.
Fgraft FCFV - FCOI =
Fig. 1. Schematic representation of theoretic mathematic model of cross-femoral venous bypass (CFB) for iliac vein obstruction. See Appendix for explanation of abbreviations.
limbs that would result from addition of a CFB, constructed with either saphenous vein or an 8 mm diameter prosthetic conduit (the smallest graft associated with a calculated transfemoral pressure differential - 70 dyne/era 2) cause increased thrombus formation in arterial PTFE grafts because of platelet activation at these levels. Assuming a similar event occurs with PTFE prostheses in the venous system, 19 o u r model demonstrates that 4 and 6 mm diameter PTFE grafts would be highly thrombogenie (Table III), in addition to their being unable to accommodate femoral venous flow at normal venous pressure gradients (Table I). For normal or low shear stresses (< 30 dyne/cm2), pseudointimal thickening increases as shear stress and velocity are decreased, which may become relevant in excessively large grafts. ~7 Based on the thickness of pseudointima Binns et al.17 measured in 8 mm arterial grafts, and the finding by Sharp et al. ~° that this layer is usually 200 Izm thicker in venous grafts, an 8 mm PTFE graft could conceivably have its luminal diameter reduced by greater than 1 mm once luminal healing is complete. Our model suggests that the hemodynamic efficacy of this originally 8 mm CFB graft would ultimately be reduced because of the pressure gradients associated with a functional CFB graft diameter now < 7 mm, and complete relief of venous hypertension would require a greater dependence on collateral flow. Therefore when considering the cross-femoral venous pressure gradients generated by physical dimensions of CFB conduits and diameter mismatch at the inflow anastomosis, as well as wall shear stresses and pseudointimal thickness, a 10 mm graft would seem to be the most appropriate prosthetic CFB conduit. To improve long-term patency of PTFE grafts, the data from the clinical and experimental surgical literature suggest that external stenting, temporary adjunctive arteriovenous fistulas, perioperative heparin, and chronic anticoagulation or antiplatelet therapy are necessary; endothelial seeding may also prove to be beneficial. 2"4"s'1°'19 We feel that the clinical decision to use a saphenous vein or a prosthetic CFB graft can be made using similar calculations with preoperative measurement of saphenous vein and CFV diameters, CFB flows in the contralateral normal limb, and femoral venous pressure gradients. (Since treadmill exercise would be precluded in patients with femoral vein catheters, exercise-induced venous flow augmentation could be simulated by the reactive hyperemia
induced by inflow occlusion with a cuff inflated to 300 mm Fig for 3 minutes and released. 6) Postoperative femoral pressure measurements are essential to establish the hemodynamic efficacy of CFB procedures. REFERENCES
1. Palma EC, Esperon R. Vein transplants and grafts in the surgical treatment of the postphlebitic syndrome. J Cardiovasc Surg 1960;1:94-107. 2. Lalka SG, Malone JM. Surgical management of chronic obstructive venous disease of the lower extremity. In: Rutherford RB, ed. Vascular surgery. Philadelphia: WB Saunders Co, 1989:1627-47. 3. Halliday P, Harris J, May J. Femoro-femoral crossover grafts (Palma operation): a long-term follow-up study. In: Bergan JJ, Yao JST, eds. Surgery of the veins. Orlando: Grune & Stratton, Inc, 1985:241-59. 4. Eldof B. Temporary arteriovenous fistula in reconstruction of iliac vein obstruction using PTFE grafts. In: Eklof B, Gjores JE, Thulesius O, Bergqvist D, eds. Controversies in the management of venous disorders. London: Butterworths, 1989:280-90. 5. Ijima H, Kodama M, Hori M. Temporary arteriovenous fistula for venous reconstruction using synthetic graft: a clinical and experimental investigation. J Cardiovasc Surg 1985;26:131-6. 6. Raju S. New approaches to the diagnosis and treatment of venous obstruction. J VASC SURG 1986;4:42-54. 7. Aschberg S, Ankarcrona H, Bergstrand O, Bjorkholm M. Temporary arterio-venous shunts to dilate saphenous crossover grafts and maintain graft patency. Acta Chit Scand 1976;142:585-7. 8. Negus D, Cockett FB. Femoral vein pressures in postphlebitic ifiac vein obstruction. Br J Surg 1967;54:522-5. 9. Browse NL, Burnand KG, Thomas ML. Diseases of the veins. London: Edward Arnold, 1988:271-87. 10. May R, DeWeese J'A. Surgery of the pelvic veins. In: May R, ed. Surgery of the veins of the leg and pelvis. Philadelphia: WB Sannders Co, 1979:158-84. 11. Vollmar J. Reconstruction of the iliac veins and inferior vena cava. In:Hobbs JT, ed. The treatment of venous disorders. London: MTP Press, 1977:321-44. 12. May R. The Palma operation with Gottlob's endothelium preserving suture. In: May R, Weber J, eds. Pelvic and abdominal veins: progress in diagnostics and therapy. Amsterdam: Excerpta Medica, 1981:192-7. 13. Lalka SG, Unthank JL, Lash JM, McGue JG, Cikrit DF, Dalsing MC. Hemodynamic effects of varied graft diameters in the venous system. Surgery 1991 (In press). 14. Wright CB, Hobson RW. Hemodynamic effects of femoral venous occlusion in the subhuman primate. Surgery 1974; 75:453-60. 15. Mayor GE, Galloway JMD. Collaterals of the deep venous circulation of the lower limb. Surg Gynecol Obstet 1967; 125:561-71. 16. Gruss JD, Vargas-Montano H, Barrels D, Hanschke D, Fietzo-Fischer B. Direct reconstructive venous surgery. Int Angiol 1985;4:441-53. 17. Birms RL, Ku DN, Stewart NIT, Ansley JP, Coyle KA. Optimal graft diameter: Effect of wall shear stress on vascular healing. J VASCSURG 1989;10:326-37.
Volume 13 Number 5 May 1991
Saphenous vein for venous bypass 629
18. Scherck JP, Kerstein MD, Stansel HC. The current status of vena caval replacement. Surgery 1974;76:209-33. 19. Gloviczki P, Hollier LH, Dewanjee MK, Trastek VF, Hoffman EA, Kaye MP. Experimental replacement of the inferior vena cava: factors affecting patency. J VAsc SURG 1984;95:657-66. 20. Sharp WV, McVay WP, Flaksman RJ, Wright J. Electrolour: achievement of long-term vascular tolerance. Surg Forum 1969;20:141-2. Submitted Oct. 9, 1990; accepted Dec. 27, 1990.
APPENDIX The theoretic resistance of a native or prosthetic conduit was calculated by use of the equation:
In vivo, a certain amount o f pressure would be recovered as the blood enters the slow velocity recipient vein. However, the precise magnitude of the recovered pressure would be dependent on the pressure and flow in the contralateral limb. Therefore, dP B represents the maximal pressure gradient created across the inflow anastomosis as a result of a femoral vein/graft diameter mismatch. This calculation simply serves to illustrate the potential size of this pressure gradient, as presented in Table II. Subsequent calculations do not include consideration o f d P B. The maximum flow (Fsvmax) that could be accommodated by each saphenous vein at pressure gradients equal to the clinical normal standards of 4 m m H g (533 N/m2) at rest and 6 mm H g (800 N/m2) after exercise (dPstd) were calculated as follows:
VxI×8 Rgrafr :
3.14 x rgr~4
where the viscosity of blood (V) in the venous circulation is assumed to be 0.01 N × sec/m 2, graft length (1) is 0.20 m, and rgraft is the radius of the graft in m, and 3.14 is an approximation of pi. Peak (in time) volume flow in the femoral vein (FcF v in L/min) was calculated for each subject by use of the measured radius of the femoral vein (rcFv in m) and the measured mid-vessel peak flow velocity (Vme~ in m/sec). Assuming a parabolic velocity profile, the peak instantaneous spatial-averaged velocity (vvc~) of flow was assumed to be approximately 50% of v m.... which may underestimate the true v ~ a because of the expected blunt velocity profile of a large diameter vein: Vpeak = 0 . 5 X V. . . . FCF v = Vpeak × 3 . 1 4 × r c r v 2
(2)
(3)
Although Vpe~ underestimates the average flow velocity across the lumen of the vessel, FcF v most likely overestimates resting total flow, because o f the intermittent nature of venous flow at rest. Venous flow is expected to be less intermittent in nature and to have a more parabolic velocity profile during periods of hyperemia; therefore FcF v calculated for postexercise conditions is expected to more accurately reflect the time-averaged total venous flow under these conditions. The theoretic pressure gradient across a graft accommodating a flow equivalent to the normal femoral venous flow was calculated by use o f the peak FcF v as calculated in (3): dPgraft = Rgrafr X FCF v
(4)
The Bernoulli equation was used to account for the additional potential pressure gradient (dPB) across the inflow anastomosis as a result of a graft/vein diameter mismatch. The density of blood (z) was assumed to be 1052 kg/m3: Vgraft = Vpeak X rcrv2/rg~ft2 dP B = 0.5 x z x (Vgraft 2 -- Vpeak 2)
Fsvmax = dPstJRsv
(l)
(5) (6)
(7)
The fraction of preobstruction CFV flow (FcFv) that would have to be accommodated by collaterals to have a postoperative gradient _
basis for selecting saphenous vein or a larger diameter prosthetic cross-femoral venous bypass graft for relief of obstructive venous hypertension. Common femoral vein resting and postexercise peak flows, and common femoral vein and saphenous vein diameters were measured in 18 healthy individuals and used to estimate the pressure gradient (dP) across 20 cm long cross-femoral venous bypass grafts of sapbenous vein or 4, 6, 8, 10, and 12 mm prosthetic conduits, in the presence of a transpelvic venous collateral network of varied cross section. The upper limits of normal for the gradients in our model (dPs,a) were set at 4 mm Hg for resting flows and 6 mm Hg after exercise. Mean sapbenous vein diameter was 4.3 +- 0.22 ram, which was 36.5% +- 1.73% of common femoral vein diameter. When the saphenous veins of two thirds of the individuals in our study were used as theoretic cross-femoral venous bypass conduits, > 80% of postobstruction peak cross-femoral venous bypass graft flow had to be carried by collaterals to maintain a gradient < dPst a. We demonstrated that 4.5 to 6.0 mm diameter saphenous cross-femoral venous bypass grafts would be bemodynamically efficacious in refieving venous hypertension, but only when implanted in parallel with an existing venous collateral network that limited the preoperative dI' to 4.5 to 7.5 mm Hg at resting flows and 7.0 to 11.5 nun Hg after exercise; only 44% ofsapbenous veins were adequate for cross-femoral venous bypass grafts by these criteria. Prosthetic cross-femoral venous bypass conduits of > 8 mm diameter eliminated venous hypertension even in the absence of collateral venous flow. ( J VAse Suv.~ 1991;13:622-30.)
Cross-femoral venous bypass (CFB) grafting for unilateral iliofemoral venous occlusion was introduced by Palma and Esperon ~ 30 years ago. Since then the literature records almost 400 o f these procedures performed for a variety o f indications: chronic venous hypertension resulting from remote iliofemoral deep venous thrombosis (most cases), incomplete restoration o f venous outflow after venous thrombectomy for acute iliofemoral thrombosis, trauma, iatrogenic operative injury, pelvic tumor ingrowth or extrinsic compression, radiation sequelae, retroperitoneal fibrosis, and "iliac vein compression syndrome" from the right c o m m o n iliac
From the Departments of Surgery, and Physiologyand Biophysics, Indiana University School of Medicine, Indianapolis. Presented at the Fourteenth Annual Meeting of the Midwestern Vascular Surgical Society, Toledo, Ohio, Sept. 14-15, 1990. Reprint requests: Stephen G. Lalka, MD, Assistant Professor of Surgery,Indiana UniversityMedicalCenter,Wishard Memorial Hospital OPE 310A, 1001 West 10th St., Indianapolis IN 46202 24/6/27614 622
artery overlying the left c o m m o n iliac vein at the pelvic brim. 2-4 As originally described and most commonly reported, the CFB is constructed by use of the contralateral saphenous vein transposed in subcutaneous suprapubic fashion to the obstructed limb. 1"2 Although unanimous agreement exists that autogenous venous conduits in peripheral venous reconstruction have better long-term patency than synthetic grafts, some investigators have noted that saphenous vein CFB grafts often provide inadequate symptomatic relief o f venous hypertension because o f the high resistance o f the small saphenous vein conduit. 4-7 Review o f the literature suggests that the ultimate test o f significance o f an iliac vein obstruction must be the physiologic demonstration o f an increased resistance to venous outflow; the best test is the comparison o f resting and postexercise femoral vein pressures between the obstructed and contralateral normal limbs. 811 In the opinion o f Browse et al.9 and May and DeWeese, ~° no iliac vein bypass procedure
Volume 13 Number 5 May 1991
should be performed without preoperative and postoperative femoral venous pressure measurements. Unfortunately, the few surgeons who have reported series of CFB procedures have not adequately documented the relationship between saphenous CFB graft patency, reduction in venous hypertension, and symptomatic relief. 2-4"6"7"~°-~ Because of the lack of clinical hemodynamic data verifying the efficacy of saphenous vein as a CFB conduit, we developed a mathematic model of unilateral iliac vein obstruction to establish a theoretic basis for selecting saphenous vein or a larger diameter prosthetic conduit for CFB. The validity of this mathematic model has previously been confirmed by in vivo canine studies. ~s PATIENTS A N D M E T H O D S Patient data
In 18 volunteer subjects (age 24 to 40 years; 11 men/7 women), an ultrasonic duplex scanner (ATL Ultramark 4, Advanced Technology Laboratories, Bothell, Wash.) was used to measure saphenous vein cross-sectional diameter, common femoral vein (CFV) diameter, and CFV peak velocity in one limb. These saphenous veins were free of varicosities, and there was no history of previous deep venous thrombosis in these limbs. The diameters and flows were measured in supine position, both at rest and immediately after standard treadmill exercise (2.5 mph and 10% grade for 5 minutes). This level of exercise was chosen to simulate venous outflow during normal daily physical activity. Saphenous vein diameter was measured at both the high- and low-thigh levels (n = 18) at rest, but was only recorded at the low-thigh level (n = 15) after exercise to record saphenous vein and CFV diameter and CFV velocity as simultaneously as possible after exercise. Theoretic hemodynamic analyses The equations used to construct our theoretic model of cross-femoral venous bypass are described in detail in the Appendix. Refer to Fig. 1 for a schematic representation of the mathematic model. The theoretic resistances of CFB grafts constructed with each subject's saphenous vein (using the average of their resting high- and low-thigh diameters) or prosthetic conduits of 4, 6, 8, 10, and 12 nun diameter, were calculated. Preexercise and postexercise CFV volume flows were calculated for each subject by use of the measured radius of the CFV and the measured peak venous flow velocity. The Poiseuille equation was then used to determine the
Saphenous vein for venous bypass 623
theoretic pressure gradients across 20 cm segments of saphenous vein and 4 to 12 mm prosthetic conduits by use of each individual's saphenous vein diameter and CFV flow. To account for the potential pressure dissipation associated with graft/femoral vein diameter mismatch at the inflow anastomosis when using hypodiametric CFB conduits, the Bernoulli principle was used to calculate the maximal additional theoretic pressure gradient at preexercise and postexercise peak CFV flows. For our series of mathematic simulations, several assumptions were necessary: (1) arterial inflow would not be chronically altered by iliac vein obstruction, based on animal data for femoral vein occlusion14; (2) total arterial inflow in both legs is equal, therefore the total venous outflow from the obstructed limb in a patient with unilateral iliac vein occlusion should be the same as in the contralateral normal limb, after a period of outflow redistribution by recruitment of superficial and deep ipsilateral and cross-over venous collaterals (hereafter termed transpelvic collaterals)~5; (3) under normal conditions CFV flow in both legs is equal and represents the same fraction of total venous outflow, therefore we can use the CFV flow measured in normal limbs as a clinically-relevant estimate of the redistributed venous flow that would either cross a CFB or be accommodated by newly recruited venous collaterals in a limb with iliac vein obstruction; and (4) because reports of clinical femoral venous pressure data indicate that the upper limits of the normal pressure gradient between limbs is 4 mm H g at rest and 6 mm Hg after exercise, s-12 these clinical standards (dPsta) were used in our model. The maximum flow that could be accommodated by each subject's saphenous vein at pressure gradients equal t o dPsta at rest and after exercise was calculated by means of the theoretic resistance of the graft. The fraction of an individual's preobstruction CFV flow that would have to be carried by collaterals, despite the presence of a saphenous CFB graft, to achieve a normal postoperative venous pressure differential between obstructed and contralateral normal limbs was then calculated for resting and postexercise peak flOWS.
To demonstrate the effects of venous collateralization alone on the femoral venous pressure gradient between limbs (hereafter termed the transfemoral pressure differential) in a patient with unilateral iliac vein occlusion, the theoretic venous pressure gradient was calculated for a wide range of collateral crosssectional area. We then calculated the total venous pressure differential between normal and abnormal
Journ~of VASCULAR SURGERY
624 Lalka et al.
Fgraft FCFV - FCOI =
Fig. 1. Schematic representation of theoretic mathematic model of cross-femoral venous bypass (CFB) for iliac vein obstruction. See Appendix for explanation of abbreviations.
limbs that would result from addition of a CFB, constructed with either saphenous vein or an 8 mm diameter prosthetic conduit (the smallest graft associated with a calculated transfemoral pressure differential - 70 dyne/era 2) cause increased thrombus formation in arterial PTFE grafts because of platelet activation at these levels. Assuming a similar event occurs with PTFE prostheses in the venous system, 19 o u r model demonstrates that 4 and 6 mm diameter PTFE grafts would be highly thrombogenie (Table III), in addition to their being unable to accommodate femoral venous flow at normal venous pressure gradients (Table I). For normal or low shear stresses (< 30 dyne/cm2), pseudointimal thickening increases as shear stress and velocity are decreased, which may become relevant in excessively large grafts. ~7 Based on the thickness of pseudointima Binns et al.17 measured in 8 mm arterial grafts, and the finding by Sharp et al. ~° that this layer is usually 200 Izm thicker in venous grafts, an 8 mm PTFE graft could conceivably have its luminal diameter reduced by greater than 1 mm once luminal healing is complete. Our model suggests that the hemodynamic efficacy of this originally 8 mm CFB graft would ultimately be reduced because of the pressure gradients associated with a functional CFB graft diameter now < 7 mm, and complete relief of venous hypertension would require a greater dependence on collateral flow. Therefore when considering the cross-femoral venous pressure gradients generated by physical dimensions of CFB conduits and diameter mismatch at the inflow anastomosis, as well as wall shear stresses and pseudointimal thickness, a 10 mm graft would seem to be the most appropriate prosthetic CFB conduit. To improve long-term patency of PTFE grafts, the data from the clinical and experimental surgical literature suggest that external stenting, temporary adjunctive arteriovenous fistulas, perioperative heparin, and chronic anticoagulation or antiplatelet therapy are necessary; endothelial seeding may also prove to be beneficial. 2"4"s'1°'19 We feel that the clinical decision to use a saphenous vein or a prosthetic CFB graft can be made using similar calculations with preoperative measurement of saphenous vein and CFV diameters, CFB flows in the contralateral normal limb, and femoral venous pressure gradients. (Since treadmill exercise would be precluded in patients with femoral vein catheters, exercise-induced venous flow augmentation could be simulated by the reactive hyperemia
induced by inflow occlusion with a cuff inflated to 300 mm Fig for 3 minutes and released. 6) Postoperative femoral pressure measurements are essential to establish the hemodynamic efficacy of CFB procedures. REFERENCES
1. Palma EC, Esperon R. Vein transplants and grafts in the surgical treatment of the postphlebitic syndrome. J Cardiovasc Surg 1960;1:94-107. 2. Lalka SG, Malone JM. Surgical management of chronic obstructive venous disease of the lower extremity. In: Rutherford RB, ed. Vascular surgery. Philadelphia: WB Saunders Co, 1989:1627-47. 3. Halliday P, Harris J, May J. Femoro-femoral crossover grafts (Palma operation): a long-term follow-up study. In: Bergan JJ, Yao JST, eds. Surgery of the veins. Orlando: Grune & Stratton, Inc, 1985:241-59. 4. Eldof B. Temporary arteriovenous fistula in reconstruction of iliac vein obstruction using PTFE grafts. In: Eklof B, Gjores JE, Thulesius O, Bergqvist D, eds. Controversies in the management of venous disorders. London: Butterworths, 1989:280-90. 5. Ijima H, Kodama M, Hori M. Temporary arteriovenous fistula for venous reconstruction using synthetic graft: a clinical and experimental investigation. J Cardiovasc Surg 1985;26:131-6. 6. Raju S. New approaches to the diagnosis and treatment of venous obstruction. J VASC SURG 1986;4:42-54. 7. Aschberg S, Ankarcrona H, Bergstrand O, Bjorkholm M. Temporary arterio-venous shunts to dilate saphenous crossover grafts and maintain graft patency. Acta Chit Scand 1976;142:585-7. 8. Negus D, Cockett FB. Femoral vein pressures in postphlebitic ifiac vein obstruction. Br J Surg 1967;54:522-5. 9. Browse NL, Burnand KG, Thomas ML. Diseases of the veins. London: Edward Arnold, 1988:271-87. 10. May R, DeWeese J'A. Surgery of the pelvic veins. In: May R, ed. Surgery of the veins of the leg and pelvis. Philadelphia: WB Sannders Co, 1979:158-84. 11. Vollmar J. Reconstruction of the iliac veins and inferior vena cava. In:Hobbs JT, ed. The treatment of venous disorders. London: MTP Press, 1977:321-44. 12. May R. The Palma operation with Gottlob's endothelium preserving suture. In: May R, Weber J, eds. Pelvic and abdominal veins: progress in diagnostics and therapy. Amsterdam: Excerpta Medica, 1981:192-7. 13. Lalka SG, Unthank JL, Lash JM, McGue JG, Cikrit DF, Dalsing MC. Hemodynamic effects of varied graft diameters in the venous system. Surgery 1991 (In press). 14. Wright CB, Hobson RW. Hemodynamic effects of femoral venous occlusion in the subhuman primate. Surgery 1974; 75:453-60. 15. Mayor GE, Galloway JMD. Collaterals of the deep venous circulation of the lower limb. Surg Gynecol Obstet 1967; 125:561-71. 16. Gruss JD, Vargas-Montano H, Barrels D, Hanschke D, Fietzo-Fischer B. Direct reconstructive venous surgery. Int Angiol 1985;4:441-53. 17. Birms RL, Ku DN, Stewart NIT, Ansley JP, Coyle KA. Optimal graft diameter: Effect of wall shear stress on vascular healing. J VASCSURG 1989;10:326-37.
Volume 13 Number 5 May 1991
Saphenous vein for venous bypass 629
18. Scherck JP, Kerstein MD, Stansel HC. The current status of vena caval replacement. Surgery 1974;76:209-33. 19. Gloviczki P, Hollier LH, Dewanjee MK, Trastek VF, Hoffman EA, Kaye MP. Experimental replacement of the inferior vena cava: factors affecting patency. J VAsc SURG 1984;95:657-66. 20. Sharp WV, McVay WP, Flaksman RJ, Wright J. Electrolour: achievement of long-term vascular tolerance. Surg Forum 1969;20:141-2. Submitted Oct. 9, 1990; accepted Dec. 27, 1990.
APPENDIX The theoretic resistance of a native or prosthetic conduit was calculated by use of the equation:
In vivo, a certain amount o f pressure would be recovered as the blood enters the slow velocity recipient vein. However, the precise magnitude of the recovered pressure would be dependent on the pressure and flow in the contralateral limb. Therefore, dP B represents the maximal pressure gradient created across the inflow anastomosis as a result of a femoral vein/graft diameter mismatch. This calculation simply serves to illustrate the potential size of this pressure gradient, as presented in Table II. Subsequent calculations do not include consideration o f d P B. The maximum flow (Fsvmax) that could be accommodated by each saphenous vein at pressure gradients equal to the clinical normal standards of 4 m m H g (533 N/m2) at rest and 6 mm H g (800 N/m2) after exercise (dPstd) were calculated as follows:
VxI×8 Rgrafr :
3.14 x rgr~4
where the viscosity of blood (V) in the venous circulation is assumed to be 0.01 N × sec/m 2, graft length (1) is 0.20 m, and rgraft is the radius of the graft in m, and 3.14 is an approximation of pi. Peak (in time) volume flow in the femoral vein (FcF v in L/min) was calculated for each subject by use of the measured radius of the femoral vein (rcFv in m) and the measured mid-vessel peak flow velocity (Vme~ in m/sec). Assuming a parabolic velocity profile, the peak instantaneous spatial-averaged velocity (vvc~) of flow was assumed to be approximately 50% of v m.... which may underestimate the true v ~ a because of the expected blunt velocity profile of a large diameter vein: Vpeak = 0 . 5 X V. . . . FCF v = Vpeak × 3 . 1 4 × r c r v 2
(2)
(3)
Although Vpe~ underestimates the average flow velocity across the lumen of the vessel, FcF v most likely overestimates resting total flow, because o f the intermittent nature of venous flow at rest. Venous flow is expected to be less intermittent in nature and to have a more parabolic velocity profile during periods of hyperemia; therefore FcF v calculated for postexercise conditions is expected to more accurately reflect the time-averaged total venous flow under these conditions. The theoretic pressure gradient across a graft accommodating a flow equivalent to the normal femoral venous flow was calculated by use o f the peak FcF v as calculated in (3): dPgraft = Rgrafr X FCF v
(4)
The Bernoulli equation was used to account for the additional potential pressure gradient (dPB) across the inflow anastomosis as a result of a graft/vein diameter mismatch. The density of blood (z) was assumed to be 1052 kg/m3: Vgraft = Vpeak X rcrv2/rg~ft2 dP B = 0.5 x z x (Vgraft 2 -- Vpeak 2)
Fsvmax = dPstJRsv
(l)
(5) (6)
(7)
The fraction of preobstruction CFV flow (FcFv) that would have to be accommodated by collaterals to have a postoperative gradient _
